Erdős Problem 203

Reference: erdosproblems.com/203

theorem Erdos203.erdos_203 : (∃ (m : ℕ), m.Coprime 6 ∧ ∀ (k l : ℕ), ¬Nat.Prime (2 ^ k * 3 ^ l * m + 1)) ↔ sorry

Is there an integer $m$ with $(m, 6) = 1$ such that none of $2^k \cdot 3^\ell \cdot m + 1$ are prime, for any $k, \ell \ge 0$?